It is true that some people have problems with pedal tones. I've known
of people who have done pedal tones once and had to spend the following
few days to recover. But I don't think that this is neccesarrily caused
by which embouchure is used. The "big picture" is much too complex to simplify
it to that level.

I use pedal tones for two different reasons and both reasons require
different techniques and embouchures. To me, they are two different exercises.

The first reason, why I use pedal tones is to get more blood circulating
through the lips. For this purpose, I use the easier fingerings and an
embouchure which is not at all similar to my normal embouchure. When I
do these, the object is to descend chromatically untill I go as low as
I can. Lately, with the mouthpiece I've been using, my lowest note is Gb
concert, two octaves below the lowest "true Gb".

But that is entirely different from the other pedal tones which I also
do on a regular basis. This other set of pedals is for the purpose of helping
me learn to control my pitch and air. For these pedal tones, I use the
same fingerings as the octave above and I use the exact same embouchure
as my normal playing. The object for this set of exercises is to play the
pedal C, B, Bb and A as if they are normal notes. This is very difficult
to do at first because those notes don't slot with those fingerings.

My point is that there are entirely different approaches to pedal tones
which have entirely different effects on different people. My advice is
to try different things until you find what works for you. Don't automatically
rule out "different" approaches just because they don't work for other
people.